How can I use autoencoders to analyze patterns and classify them?
When using an autoencoder, I believe the data u feed in has to be correlated in one way or another. For example, If i want to learn a latent representation of an image of a cat, The training data that I feed into the autoencoder should constitute only cat images. 

Similar to other neural networks, you feed the autoencoder with a set of training data and hope that the network learns a set of weights that is able to output from the latent representation the exact image. To see whether the weights learnt by the autoencoder is able to generalise to other unseen cat images, you would have to use a test set for this. 

Here is a paper about autoencoding. https://web.stanford.edu/class/cs294a/sparseAutoencoder_2011new.pdf

I hope this helps you somewhat in deciding whether you should use an autoencoder.